[math-fun] Fabricating a glass/crystal sphere circa 1500
I watched a transit of Venus through an ~8" reflector made by Aerobie|Aeropress inventor Alan Adler, who precisely strained spherical mirrors. The editor of Sky & Telescope was very enthused, but the technique never caught on, apparently because CNC grinding of paraboloids got cheap. Alan is now using his extra mirrors under homemade tungsten tops that spin for twenty minutes. What is the optimal shape to trade air drag for moment of inertia? It turns out to be hard to model air drag. --rwg On 2017-10-23 14:37, Richard Howard wrote:
Large telescope mirrors start as extremely accurate sections of a sphere made by carefully randomized grinding of two surfaces against each other. The only two surfaces that fit together in all orientations are spheres.
Starting with a rough glass sphere and a rough hemispherical hole in a plate, continued random grinding produces a perfect sphere (and a perfect hemispherical hole).
BTW, the thermal approaches have the difficulty of dealing with the thermal expansion of glass. A 8" sphere could take many months to anneal without shattering. Corning museum has a nice video of making of the largest glass paperweight (~13" diameter and over 109 lbs).
--R
On Mon, Oct 23, 2017 at 1:58 PM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
It was perhaps 58 years ago, in our High School auditorium, the speaker gave us a demo of this prestressed glass phenomenon. It was in the shape of a chemist's Florence flask, the rounded kind. He first used the flask to hammer a nail, no problem. Then he dropped in a speck of carborundum. It's harder than glass, and produces a tiny nick on impact. The flask just exploded.
-- Gene
On Monday, October 23, 2017, 1:29:12 PM PDT, Bill Gosper < billgosper@gmail.com> wrote:
Interesting 16/sec ball bearing production process: https://www.youtube.com/watch?v=19duYMdiXi0 Falling raindrops form cabochons: https://www.youtube.com/watch?v=a9CRrGvQwe0 1961|2 freshman chemistry lecturer demoed Prince Rupert's Drops, and then something more interesting. (Prince <othername>'s Drops? Google fails me.) Hollow, thick-walled glass blobs, open at one end. He hammered nails with one, then wrapped it in a towel, dropped in some carborundum crumbs, BAM! --rwg
On 2017-10-22 11:57, Dan Asimov wrote:
Henry got that right — in fact, something quite interesting happens, as Wikipedia says:
----- Prince Rupert's Drops (also known as Dutch or Batavian tears) are toughened glass beads created by dripping molten glass into cold water, which causes it to solidify into a tadpole-shaped droplet with a long, thin tail. These droplets are characterized internally by very high residual stresses, which give rise to counter-intuitive properties, such as the ability to withstand a blow from a hammer or a bullet on the bulbous end without breaking, while exhibiting explosive disintegration if the tail end is even slightly damaged. In nature, similar structures are produced under certain conditions in volcanic lava. -----
more at https://en.wikipedia.org/wiki/Prince_Rupert's_Drop.
—Dan
If you want to cheat and make a perfect parabola for a telescope mirror, it is hard to beat the spinning liquid trick. Mercury work well, if you want to only look up, but epoxy is more versatile (and less toxic). In the 60's I made a 120" f/1 mirror at Cal Tech out of epoxy poured on a roughly parabolic form and spun on air bearings. This mirror and its 60" brothers did the first IR sky surveys looking for dim stars, molecular clouds, etc. The parabola you get by spinning is not quite perfect enough for first-class optical imaging, but just fine for 2-10 micron IR. --R On Wed, Oct 25, 2017 at 9:05 PM, Bill Gosper <billgosper@gmail.com> wrote:
I watched a transit of Venus through an ~8" reflector made by Aerobie|Aeropress inventor Alan Adler, who precisely strained spherical mirrors. The editor of Sky & Telescope was very enthused, but the technique never caught on, apparently because CNC grinding of paraboloids got cheap. Alan is now using his extra mirrors under homemade tungsten tops that spin for twenty minutes. What is the optimal shape to trade air drag for moment of inertia? It turns out to be hard to model air drag. --rwg
On 2017-10-23 14:37, Richard Howard wrote:
Large telescope mirrors start as extremely accurate sections of a sphere made by carefully randomized grinding of two surfaces against each other. The only two surfaces that fit together in all orientations are spheres.
Starting with a rough glass sphere and a rough hemispherical hole in a plate, continued random grinding produces a perfect sphere (and a perfect hemispherical hole).
BTW, the thermal approaches have the difficulty of dealing with the thermal expansion of glass. A 8" sphere could take many months to anneal without shattering. Corning museum has a nice video of making of the largest glass paperweight (~13" diameter and over 109 lbs).
--R
On Mon, Oct 23, 2017 at 1:58 PM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
It was perhaps 58 years ago, in our High School auditorium, the speaker gave us a demo of this prestressed glass phenomenon. It was in the shape of a chemist's Florence flask, the rounded kind. He first used the flask to hammer a nail, no problem. Then he dropped in a speck of carborundum. It's harder than glass, and produces a tiny nick on impact. The flask just exploded.
-- Gene
On Monday, October 23, 2017, 1:29:12 PM PDT, Bill Gosper < billgosper@gmail.com> wrote:
Interesting 16/sec ball bearing production process: https://www.youtube.com/watch?v=19duYMdiXi0 Falling raindrops form cabochons: https://www.youtube.com/watch?v=a9CRrGvQwe0 1961|2 freshman chemistry lecturer demoed Prince Rupert's Drops, and then something more interesting. (Prince <othername>'s Drops? Google fails me.) Hollow, thick-walled glass blobs, open at one end. He hammered nails with one, then wrapped it in a towel, dropped in some carborundum crumbs, BAM! --rwg
On 2017-10-22 11:57, Dan Asimov wrote:
Henry got that right — in fact, something quite interesting happens, as Wikipedia says:
----- Prince Rupert's Drops (also known as Dutch or Batavian tears) are toughened glass beads created by dripping molten glass into cold water, which causes it to solidify into a tadpole-shaped droplet with a long, thin tail. These droplets are characterized internally by very high residual stresses, which give rise to counter-intuitive properties, such as the ability to withstand a blow from a hammer or a bullet on the bulbous end without breaking, while exhibiting explosive disintegration if the tail end is even slightly damaged. In nature, similar structures are produced under certain conditions in volcanic lava. -----
more at https://en.wikipedia.org/wiki/Prince_Rupert's_Drop.
—Dan
math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
What is the shape of a circular diaphragm deformed by air pressure? Is it more paraboloidal than spherical, or less? In any event, you should be able to crudely grind the back side before sucking it down. Using liquid, not air, lest you accidentally build a barometer. --rwg On Wed, Oct 25, 2017 at 6:05 PM, Bill Gosper <billgosper@gmail.com> wrote:
I watched a transit of Venus through an ~8" reflector made by Aerobie|Aeropress inventor Alan Adler, who precisely strained spherical mirrors. The editor of Sky & Telescope was very enthused, but the technique never caught on, apparently because CNC grinding of paraboloids got cheap. Alan is now using his extra mirrors under homemade tungsten tops that spin for twenty minutes. What is the optimal shape to trade air drag for moment of inertia? It turns out to be hard to model air drag. --rwg
On 2017-10-23 14:37, Richard Howard wrote:
Large telescope mirrors start as extremely accurate sections of a sphere made by carefully randomized grinding of two surfaces against each other. The only two surfaces that fit together in all orientations are spheres.
Starting with a rough glass sphere and a rough hemispherical hole in a plate, continued random grinding produces a perfect sphere (and a perfect hemispherical hole).
BTW, the thermal approaches have the difficulty of dealing with the thermal expansion of glass. A 8" sphere could take many months to anneal without shattering. Corning museum has a nice video of making of the largest glass paperweight (~13" diameter and over 109 lbs).
--R
On Mon, Oct 23, 2017 at 1:58 PM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
It was perhaps 58 years ago, in our High School auditorium, the speaker gave us a demo of this prestressed glass phenomenon. It was in the shape of a chemist's Florence flask, the rounded kind. He first used the flask to hammer a nail, no problem. Then he dropped in a speck of carborundum. It's harder than glass, and produces a tiny nick on impact. The flask just exploded.
-- Gene
On Monday, October 23, 2017, 1:29:12 PM PDT, Bill Gosper < billgosper@gmail.com> wrote:
Interesting 16/sec ball bearing production process: https://www.youtube.com/watch?v=19duYMdiXi0 Falling raindrops form cabochons: https://www.youtube.com/watch?v=a9CRrGvQwe0 1961|2 freshman chemistry lecturer demoed Prince Rupert's Drops, and then something more interesting. (Prince <othername>'s Drops? Google fails me.) Hollow, thick-walled glass blobs, open at one end. He hammered nails with one, then wrapped it in a towel, dropped in some carborundum crumbs, BAM! --rwg
On 2017-10-22 11:57, Dan Asimov wrote:
Henry got that right — in fact, something quite interesting happens, as Wikipedia says:
----- Prince Rupert's Drops (also known as Dutch or Batavian tears) are toughened glass beads created by dripping molten glass into cold water, which causes it to solidify into a tadpole-shaped droplet with a long, thin tail. These droplets are characterized internally by very high residual stresses, which give rise to counter-intuitive properties, such as the ability to withstand a blow from a hammer or a bullet on the bulbous end without breaking, while exhibiting explosive disintegration if the tail end is even slightly damaged. In nature, similar structures are produced under certain conditions in volcanic lava. -----
more at https://en.wikipedia.org/wiki/Prince_Rupert's_Drop.
—Dan
The article on flexed mirrors and the program to design them is available at the Sky and Telescope website. The process begins with grinding a spherical mirror. Then a puller plate is glued to the back of the mirror. The puller is a rigid disc, typically about 80% of the diameter of the mirror and glued to the back of the mirror with an interleaving layer of sponge rubber to distribute the pull evenly. The perimeter of the mirror is supported by a shallow cup with a cushion of sponge rubber between the mirro and the rim of the cup. A bolt attached to the puller plate passes through a hole in the bottom of the cup, then through a coil spring, a washer and a nut. The nut is tightened to pull. My 8" f6 mirror was about 0.65 inches thick and only required about 60 lbs pull. The deflection was about 5 wavelengths of light. The resultant paraboloid is accurate to about 1/20 wave. A surprising thing is that the deflection is stable, thanks to the coil spring. I star test my scope when seeing is good, and haven't seen a need to change the pull in decades. Alan Adler From: Bill Gosper <billgosper@gmail.com> To: math-fun@mailman.xmission.com Sent: Saturday, November 18, 2017 4:23 PM Subject: Re: [math-fun] Fabricating a glass/crystal sphere circa 1500 What is the shape of a circular diaphragm deformed by air pressure? Is it more paraboloidal than spherical, or less? In any event, you should be able to crudely grind the back side before sucking it down. Using liquid, not air, lest you accidentally build a barometer. --rwg On Wed, Oct 25, 2017 at 6:05 PM, Bill Gosper <billgosper@gmail.com> wrote: I watched a transit of Venus through an ~8" reflector made by Aerobie|Aeropress inventor Alan Adler, who precisely strained spherical mirrors. The editor of Sky & Telescope was very enthused, but the technique never caught on, apparently because CNC grinding of paraboloids got cheap. Alan is now using his extra mirrors under homemade tungsten tops that spin for twenty minutes. What is the optimal shape to trade air drag for moment of inertia? It turns out to be hard to model air drag. --rwg On 2017-10-23 14:37, Richard Howard wrote:
Large telescope mirrors start as extremely accurate sections of a sphere made by carefully randomized grinding of two surfaces against each other. The only two surfaces that fit together in all orientations are spheres.
Starting with a rough glass sphere and a rough hemispherical hole in a plate, continued random grinding produces a perfect sphere (and a perfect hemispherical hole).
BTW, the thermal approaches have the difficulty of dealing with the thermal expansion of glass. A 8" sphere could take many months to anneal without shattering. Corning museum has a nice video of making of the largest glass paperweight (~13" diameter and over 109 lbs).
--R
On Mon, Oct 23, 2017 at 1:58 PM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
It was perhaps 58 years ago, in our High School auditorium, the speaker gave us a demo of this prestressed glass phenomenon. It was in the shape of a chemist's Florence flask, the rounded kind. He first used the flask to hammer a nail, no problem. Then he dropped in a speck of carborundum. It's harder than glass, and produces a tiny nick on impact. The flask just exploded.
-- Gene
On Monday, October 23, 2017, 1:29:12 PM PDT, Bill Gosper < billgosper@gmail.com> wrote:
Interesting 16/sec ball bearing production process: https://www.youtube.com/watch? v=19duYMdiXi0 Falling raindrops form cabochons: https://www.youtube.com/watch? v=a9CRrGvQwe0 1961|2 freshman chemistry lecturer demoed Prince Rupert's Drops, and then something more interesting. (Prince <othername>'s Drops? Google fails me.) Hollow, thick-walled glass blobs, open at one end. He hammered nails with one, then wrapped it in a towel, dropped in some carborundum crumbs, BAM! --rwg
On 2017-10-22 11:57, Dan Asimov wrote:
Henry got that right — in fact, something quite interesting happens, as Wikipedia says:
----- Prince Rupert's Drops (also known as Dutch or Batavian tears) are toughened glass beads created by dripping molten glass into cold water, which causes it to solidify into a tadpole-shaped droplet with a long, thin tail. These droplets are characterized internally by very high residual stresses, which give rise to counter-intuitive properties, such as the ability to withstand a blow from a hammer or a bullet on the bulbous end without breaking, while exhibiting explosive disintegration if the tail end is even slightly damaged. In nature, similar structures are produced under certain conditions in volcanic lava. -----
more at https://en.wikipedia.org/wiki/ Prince_Rupert's_Drop.
—Dan
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You can get a 1 ton 40" sphere for just 19K. https://www.amazon.com/sphere/dp/B0775ZF62T/ On Wed, Oct 25, 2017 at 8:05 PM, Bill Gosper <billgosper@gmail.com> wrote:
I watched a transit of Venus through an ~8" reflector made by Aerobie|Aeropress inventor Alan Adler, who precisely strained spherical mirrors. The editor of Sky & Telescope was very enthused, but the technique never caught on, apparently because CNC grinding of paraboloids got cheap. Alan is now using his extra mirrors under homemade tungsten tops that spin for twenty minutes. What is the optimal shape to trade air drag for moment of inertia? It turns out to be hard to model air drag. --rwg
On 2017-10-23 14:37, Richard Howard wrote:
Large telescope mirrors start as extremely accurate sections of a sphere made by carefully randomized grinding of two surfaces against each other. The only two surfaces that fit together in all orientations are spheres.
Starting with a rough glass sphere and a rough hemispherical hole in a plate, continued random grinding produces a perfect sphere (and a perfect hemispherical hole).
BTW, the thermal approaches have the difficulty of dealing with the thermal expansion of glass. A 8" sphere could take many months to anneal without shattering. Corning museum has a nice video of making of the largest glass paperweight (~13" diameter and over 109 lbs).
--R
On Mon, Oct 23, 2017 at 1:58 PM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
It was perhaps 58 years ago, in our High School auditorium, the speaker gave us a demo of this prestressed glass phenomenon. It was in the shape of a chemist's Florence flask, the rounded kind. He first used the flask to hammer a nail, no problem. Then he dropped in a speck of carborundum. It's harder than glass, and produces a tiny nick on impact. The flask just exploded.
-- Gene
On Monday, October 23, 2017, 1:29:12 PM PDT, Bill Gosper < billgosper@gmail.com> wrote:
Interesting 16/sec ball bearing production process: https://www.youtube.com/watch?v=19duYMdiXi0 Falling raindrops form cabochons: https://www.youtube.com/watch?v=a9CRrGvQwe0 1961|2 freshman chemistry lecturer demoed Prince Rupert's Drops, and then something more interesting. (Prince <othername>'s Drops? Google fails me.) Hollow, thick-walled glass blobs, open at one end. He hammered nails with one, then wrapped it in a towel, dropped in some carborundum crumbs, BAM! --rwg
On 2017-10-22 11:57, Dan Asimov wrote:
Henry got that right — in fact, something quite interesting happens, as Wikipedia says:
----- Prince Rupert's Drops (also known as Dutch or Batavian tears) are toughened glass beads created by dripping molten glass into cold water, which causes it to solidify into a tadpole-shaped droplet with a long, thin tail. These droplets are characterized internally by very high residual stresses, which give rise to counter-intuitive properties, such as the ability to withstand a blow from a hammer or a bullet on the bulbous end without breaking, while exhibiting explosive disintegration if the tail end is even slightly damaged. In nature, similar structures are produced under certain conditions in volcanic lava. -----
more at https://en.wikipedia.org/wiki/Prince_Rupert's_Drop.
—Dan
math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (4)
-
Alan Adler -
Bill Gosper -
Ed Pegg Jr -
Richard Howard